Hi.
Yes and no.
1. Yes, some supermarkets do sell vegetarian and vegan pet food. Domestic cats aren't that different to large cats in their dietry requirements.
The food has to be well fortified with nutrients like Taurine that are often missing in plants but essential in a carnivores diet. Where you get these nutrients from is a bit of problem - you could just extract it from meat but it's not commonly found in plants. If you spend enough money then you could synthesize it from non-animal sources (In the laboratory taurine can be produced by alkylation of ammonia with bromoethanesulfonate salts - taken from Wikipedia, https://en.wikipedia.org/wiki/Taurine#Synthesis ). Note that there are MANY nutrients which would have to be added, I don't know all of them nor do I have the time to list them all.
2. No, it's extremely difficult and quite likely to lead to serious deficiencies in the animal and serious ill-health up to and including death of the animal. In particular, domestic cats are known to be extremely vulnerable to a condition called DCM (Dilated Cadiomyopathy) that results from a deficiency of Taurine.
As regards keeping domestic cats as pets, simply purchasing Vegetarian or Vegan cat food under the naive assumption that the cat food manufacturer have ensured nutritional adequacy may NOT be sufficient to avoid prosecution under the law for neglect and inadequate care of the animal. Many commercially available vegetarian pet foods are NOT sufficient and could only be used to replace some meals but not all of them, despite claims made by some manufacturers.
I appreciate that large cats aren't "pets" but you stated this:
Feeding animals such as big cats...
Which suggested that animals might be in a zoo or are owned and cared for in some capacity by human beings. There is then some animal welfare law which applies:
“In the UK, under the Animal Welfare Act the owner has the obligation to feed the animal an appropriate diet,” says Daniella Dos Santos, the president of the British Veterinary Association (BVA) “If your personal belief system means you don’t want to eat any animal protein, that’s fine, but that diet is not designed to meet the welfare standards of your pet.
[quote taken from a BBC article "Can you feed your dogs and cats a vegan diet?",
https://www.bbc.com/future/article/20200304-can-you-feed-cats-and-dogs-a-vegan-diet]
That article goes on to suggest that if you do feed your domestic cats a vegetarian diet then you should have their health and diet checked and advised by a qualified veterinary specialist and failure to do so could make you liable for prosecution under the animal welfare act (although I don't know of any cases of this kind that have been taken to court so far).
3. Large cats are natural carnivores and predators. There may be all sorts of harm done to them if they are not fed on something with the proper texture, smell and all other properties of meat but instead they were just given some kind of "mushy" stuff. It may be necessary for them to tear meat and chew on bones to keep their teeth and claws filed down and in good condition, for example. There may be significant harm done to the natural behaviour routines of the animal: Specifically, a large cat may become distressed if it is not able to engage in its natural behaviour. A mother and cubs may not bond adequately if the mother does not need to tear meat for the cubs etc.
Overall Summary: It does not seem advisable to switch a large cat to an entirely vegetarian diet. We probably don't have sufficient food technology to produce a satisfactory meat alternative in an economically feasible way. There may be animal welfare regulations that prohibit any attempt, at least without direct supervision and advice of experts.
Best Wishes.